dgeqrf.f(3) LAPACK dgeqrf.f(3)
subroutine dgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
subroutine dgeqrf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA,
double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerLWORK,
DGEQRF computes a QR factorization of a real M-by-N matrix A:
A = Q * R.
M is INTEGER
The number of rows of the matrix A. M >= 0.
N is INTEGER
The number of columns of the matrix A. N >= 0.
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU is DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK is INTEGER
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v**T
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
Definition at line 137 of file dgeqrf.f.
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Version 3.4.2 Tue Sep 25 2012 dgeqrf.f(3)